Ternary Eutectic System

Mixtures of three distinct materials often melt and solidify in a ternary eutectic relationship.
A good and very important geological example is the system quartz-anorthite-K-feldspar. If
you understand binary eutectics well, ternary eutectics are very
straightforward. Since ternary systems are plotted on triangle diagrams, a little review
of triangle diagrams is in order first.

Triangle Diagrams

In a triangle plot, each vertex represents 100% of a component and
the opposite edge represents zero. Point X is 28% of the way from the
bottom to the top of the diagram so it has 28% A. It's 11% of the way
from edge A-B to C, so it has 11% C.

Percentages are measured perpendicular to the zero edge. A horizontal
line through X represents compositions with 28%A and varying amounts of
B and C.

A line representing a constant ratio of two components starts at the
third vertex. The red line represents a 4/1 ratio of C to B.

All possible mixtures of compositions P and Q lie on the line between
them. R is 3/4 of the way toward P, so it represents 75% P and 25% Q.

Ternary Eutectics

A eutectic diagram involving three components actually represents
four dimensions: the three components plus temperature.

Consider the three binary systems A-B, B-C, and C-A. We can
arrange the three diagrams in three dimensions as shown here. As long as
we only consider two components, we can work with the binary diagrams as
usual.

If a system just consists of two components, we can ignore the
triangle diagram and just consider the system as a binary eutectic. So
in three dimensions, a ternary eutectic is like three binary eutectics
enclosing a triangular prism.

The space inside the triangular prism represents systems
with all three components present. There will be a field where A
crystallizes first, a field where B crystallizes first, and one where C
crystallizes first.

In reality, there is a liquidus surface covering the
triangle and as the system cools, it will slide down the surface.

This diagram shows the relationship between temperature in
the binary systems and temperature on the triangle diagram.

Very often, temperature contours are omitted. This is not a problem if
the system is simple, but if there are maxima or minima on the liquidus
surface, the diagram becomes completely useless without contours.

The
"valleys" between fields are called cotectics.

What Might We Expect?

Here's our initial situation. A, B and C are eutectic compounds. We
have a melt whose composition is given by the hollow square: richest in
B, then in C, and poorest in A.

Since this is a simple eutectic system, there's no mixing of the
solid components. So we expect that once we cool to a certain point, one
of the three components will begin to form. In this case it's B, no
surprise considering our initial composition is richest in B. The
composition of the melt begins to migrate away from the initial
composition (hollow square).

Since we're only forming B at this point, the solid composition stays
at B. The relative amounts of melt and solid are shown by the relative
position of the melt, solid, and overall system. At this point the
system is already a little more than half solid

At some point, another compound will begin to form. Given that the
melt is next richest in C, we'd expect C to form. When the melt is near
one vertex, we can more or less predict the sequence of events, but in
the middle of the diagram, we can't be sure without actual data.

Since both B and C are forming, the melt composition has to move away
from both B and C, that is, in the general direction of A.

Also, since we are now forming C as well as B, the solid composition
shifts toward C. There is, as yet, no A, so the solid remains on B-C.

At some point, A will begin to form as well. The melt remains at
that composition while A, B and C crystallize. The solid composition
moves toward A until it reaches the initial system composition. At that
point all the melt has crystallized. The actual locations of the field
boundaries depend on experimental data. They are not necessarily in the
middle of the diagram.

Evolution of Ternary Eutectics

In the diagrams below, the overall system composition is a hollow white
square and the melt and solid compositions are shown in red and blue,
respectively. The history of the melt composition is shown in magenta and the
solid in green. Blue is used to show geometric relationships between the solid,
system, and melt compositions.

The first thing that will happen is that one component will
begin to crystallize. In this case it is B. As we remove B from the melt,
the melt composition will migrate straight away from the B corner as
shown.

Eventually the melt will hit a field boundary and then a
second component will begin to form. In this case it is C. The composition
of the melt will migrate away from both B and C in the general direction
of A. The path of the melt is shown in magenta.

Since C is now forming along with B, the solid composition migrates in
the direction of C.

The melt, system, and solid compositions always lie on a straight line
as shown.

Finally the melt reaches the ternary eutectic and all three
components begin to form. The eutectic is usually a temperature minimum so
the melt does not move once it reaches the eutectic.

Since all three components are now forming, the solid composition moves
into the interior of the triangle.

The melt, system, and solid compositions always lie on a straight line
as shown. Since the melt stays at the eutectic, the solid migrates toward
the system composition as shown in green. Once it reaches the system
composition, the entire system is solidified.

Given the rules above, we can divide the triangle into six
fields with crystallization orders as shown. Note that any order is
possible.

One important ternary system is quartz-K feldspar-plagioclase. According to
Bowen's reaction series, we expect to find plagioclase forming first in igneous
rocks, then potassium feldspar, and last of all quartz. Since a large fraction
of igneous rocks lie in the plagioclase rich corner of the diagram, we find that
order in many cases and it's a useful rule of thumb. However, in silica rich
magmas, quartz can crystallize first, and the three minerals can form in any
order depending on the composition of the magma.